Digital economy, resource distortion and low-carbon inclusive development-Evidence from the perspectives of a threshold effect and knowledge spillover effect

The low-carbon economy represents a global transformation that encompasses production methods, lifestyles, values, national interests, and the destiny of humanity. As a significant contributor to carbon emissions, China has made a momentous strategic decision on carbon peaking and neutralization, infusing momentum into the global effort to address climate change. The rapid growth of the digital economy offers a fresh approach to achieving the "double carbon" objective and advancing the development of low-carbon transformation. Based on the panel data of 30 provinces in China, this paper uses the least square method to investigate the impact of digital economy development on regional low-carbon inclusive development. It is found that there is a significant inverted U shape in the impact of the digital economy on low-carbon inclusive development and the mechanism is resource allocation and ecological inequality. The threshold test found that the role of the digital economy in promoting low-carbon inclusive development shows a marginal decreasing trend. The inverted U-shaped impact of the digital economy on low-carbon inclusive development in the eastern and coastal areas and areas with a low level of factor productivity is more significant. Based on the knowledge factor spillover perspective, we found that the impact of the digital economy on low-carbon inclusive development has a spatial spillover effect, and this effect is more obvious under the role of R&D personnel mobility.


Introduction
As global carbon emissions continue to rise, the resultant environmental challenges, including climate warming and the melting of glaciers, are intensifying, jeopardizing sustainable development.To protect our planet, it is imperative that we undertake measures to curtail carbon emissions and champion sustainable development initiatives [1,2].With the rapid development of digital technology, the digital economy has become an important engine for driving global economic development.Research on the relationship between the digital economy and carbon emissions has essentially reached a consensus: the digital economy has a positive impact on carbon emission performance, but may be constrained by government environmental policies, economic objectives, and other limitations.In the process of comprehensively promoting the modernization of China, we must recognize that China, as the largest developing country in the world, faces a series of challenges in development.Although we have made remarkable economic and social progress in the past few decades, there are still obvious weaknesses in resources, energy, environment and ecosystems.Currently, the mode of high energy consumption, high pollution, and high emission is not feasible, which may lead to the misallocation of resources and the imbalance of regional development.Therefore, promoting the low-carbon transformation of China's economy has become an important topic for economists, who believe that the fourth scientific and technological revolution represented by the digital economy is an important opportunity to promote the development of low-carbon transformation [3].However, while enjoying the convenience and efficiency brought by digital technology, we must also face its possible negative impact on the environment and ecosystem.Therefore, in the future development, we must pay more attention to the greening and sustainable development of the digital economy.According to the China Academy of Information and Communications Technology (CAIC), the scale of China's digital economy has grown rapidly from 2017 to 2021, with a five-year average growth rate of 67.3 percent.Specifically, the scale of China's digital economy has increased from 27.2 trillion yuan to 45.5 trillion yuan, and its share in GDP has risen from 32.9 percent to 39.8 percent, which shows that the development of the digital economy has become one of the main engines for low-carbon high-quality economic development.
Existing research has begun to examine the impact of the digital economy on carbon emissions and high-quality social and economic development.However, these studies fail to consider the potential negative consequences of the digital economy's growth and overlook the importance of social inclusivity.Furthermore, the existing conclusions are inconsistent, making it difficult to draw clear conclusions about the impact of the digital economy [4,5].The inherent advantages and characteristics of the digital economy, such as high permeability, rapidity, and sustainability, can effectively eliminate the excessive consumption of tangible resources and energy by traditional industries and can bring breakthroughs for inclusive and low-carbon development.Drawing from the threshold and spatial knowledge spillover perspectives, this paper delves into the impact of the digital economy on the inclusive development of low-carbon regions, particularly in terms of resource mismatch and environmental inequality.
The marginal contribution is mainly in the following three aspects.First, innovation of perspective.Compared with the previous literature [6], we not only pay attention to low carbon and economic growth but also pay attention to the socially inclusive effects brought about by the development of the digital economy.In addition, we pay more comprehensive attention to the non-linear and spatial effects of the digital economy.Therefore, from the perspectives of economic growth, social inclusion, and the three dimensions of low-carbon ecology, we measured the LCID index by the fixed basis entropy weight method, and on this basis, the nonlinear impact of the digital economy on low-carbon inclusive development is discussed, which extends the existing research literature.Second, content innovation.Compared with previous studies, pays more attention to the positive impact of the digital economy on low-carbon development, while ignoring the dual characteristics of the digital economy.This paper focuses on the double-edged sword effect of the digital economy.From the perspectives of resource mismatch and profit and loss deviation, it explores the influence mechanism of the digital economy, deepening the understanding of the path of LCID.Third, conclusion revelation.We not only pay attention to the non-linear influence and double-edged sword effect of the digital economy but also pay attention to the knowledge spillover characteristics of the digital economy.We construct the knowledge weight matrix from the perspective of R&D factor flow and based on the perspective of knowledge spillover, this paper further discusses the nonlinear spatial spillover effect of the digital economy.In addition, a series of heterogeneity analyses provide more detailed empirical evidence for national policy-making.

Literature review
The polished version of your sentence could be: This study is related to two distinct streams of literature.The first pertains to the environmental impacts of digital economy development.Current research in this area primarily centers on the effects of Information and Communication Technology (ICT) and the internet on energy consumption [7][8][9], economic growth [10], Green total factor productivity [11], and environmental sustainability [12].The literature reviewed above primarily focuses on how the application of digital technology aids in enhancing green technology innovation and low-carbon technology, thereby improving green total factor productivity and fostering sustainable development.However, these studies often overlook the aspect of social inclusive development.The essence of sustainable development is the harmonious coexistence of man and nature, so the impact on human society cannot be ignored.Therefore, most literatures mainly consider the impact of the application of digital technology from the positive side.Similar studies have also found the application of digital technology has realized the adequate replacement of traditional elements with data, and sustainable development can be achieved by improving the energy structure [13], promoting technological innovation and diffusion [14], optimizing the industrial structure [15], and improving the government's concern for the environment [16].In addition, the deepening of the internet can also contribute to green economic growth by promoting the integrated development of industries, improving the level of environmental governance enhancing the innovation ability of enterprises [17], and significantly improving regional green total factor energy efficiency by alleviating resource misallocation [11].Through the analysis, it is found that most of the literature believes that the positive impact of the application of digital technology is greater than the negative impact, and they all believe that digital technology can achieve sustainable development by improving the efficiency of resource allocation, promoting the industrial structure and enhancing the innovation ability of enterprises.However, some scholars hold different views.They are concerned about the possible negative impact of the application of digital technology, especially when the rebound effect exceeds the energy-saving effect of digital technology itself, it will lead to more severe energy consumption and carbon emissions [18,19].Meanwhile, the acceleration of digital industrialization will also increase the energy consumption of digital infrastructure in society [20].
The second branch of the literature delves into the connection between the digital economy and Low carbon transformation and development.Numerous texts have been written exploring the linkage between the digital economy and low-carbon development [13,[21][22][23].However, the literature on social inclusion analysis is relatively rare.On the one hand, some kinds of literature mainly promote low-carbon development from environmental investment and financial development driven by the digital economy, but they do not take into account the spatial spillover effects and social inclusion effects of the digital economy [24][25][26].On the other hand, the literature focuses on the driving role of innovation but ignores the nonlinear role of the digital economy, so the analysis of the characteristics of digital technology is not comprehensive enough [4,27].A small number of works of literature pay attention to the spatial spillover brought about by the digital economy, but the spatial effect of the flow of knowledge elements brought about by the development of the digital economy has not been paid attention to, which is an important aspect of the digital economy as a knowledge economy [28].Some scholars have paid attention to the impact of the digital economy on the development of carbon emissions from the international level and also found that the digital economy can promote low-carbon development through industrial upgrading and financial development, but the main conclusions are limited to linear analysis [3,29].With in-depth research and the enrichment of literature, more and more people pay attention to the positive impact of the digital economy and gradually begin to pay attention to the spatial effect and threshold effects of the digital economy.However, the evaluation of the knowledge and social inclusiveness of the digital economy is still not comprehensive enough [30][31][32].Although this literature focuses on the impact of the digital economy on low-carbon development, it mainly considers the positive side and ignores the negative impact [23] and its threshold effect [33].The perspective of the influence mechanism is that the current literature primarily focuses on improving the source low-carbon technology and the end carbon emission treatment level, while overlooking the factors of pollution inequality [34].This is also one of the important innovations of this paper.Digital technology can improve the level of regional low-carbon development by reducing the unequal level of pollution.
Based on the above analysis, it is found that the existing literature still has room for further expansion.First, the influence of a specific aspect of the digital economy on green development has been extensively studied in the past literature.Second, most studies only consider the linear relationship between the digital economy and green development in different dimensions while ignoring the double-edged sword effect of the digital economy.Third, from the perspective of mechanism analysis, little literature has studied this topic from the perspective of resource distortion and profit and loss deviation.In particular, insufficient attention has been given to the phenomenon of digital inequality, resource misallocation, and knowledge spillover that may be caused by the digital economy.Therefore, based on previous literature, this paper focuses on the double-edged sword effect of the digital economy, integrates the economy, society, and environment into a unified framework, and extends the related research issues.

Digital economy and LCID
LCID is a new development model in China that considers both economic growth and social inclusion under the constraints of the "double carbon target".As a double-edged sword, the digital economy plays an important role in economic growth, social inclusion, and ecological development.
Economic growth.The expansion of the digital economy has progressively integrated into every facet of production and daily life.Propelled by advancements in digital technologies, novel business models and formats, including e-commerce, remote collaboration, and virtual offices, have rapidly evolved.This progression has facilitated the creation of a convenient and efficient online platform for communication and trading activities among market participants.The advancement of a digital economy enhances regional communication and cooperation.It does so by diminishing local protectionist barriers and lowering the cost of information for businesses.Additionally, it boosts connectivity between different industries and amplifies the impact of information sharing and knowledge spillovers.This leads to a more optimal distribution of resources and factors across regions, ultimately fostering economic growth.The digital economy can promote economic growth in two ways.At the micro level, the digital economy can alleviate information asymmetry and reduce transaction costs [35].At the macro level, a digital economy increases the level of labor productivity in an industry or region, which in turn drives regional economic growth.Empirical research indicates that the digital economy can foster high-quality development through enhanced entrepreneurial activity and more efficient technology utilization.Nonetheless, certain scholars argue that the growth of the digital economy could result in market monopolization, adhering to the principle of "the strong getting stronger."When the development of the digital economy exceeds the extreme point, resource allocation will be distorted.The progress of digital technology can provide a good opportunity for enterprises to win market competition or even monopoly, which may hinder the development of fair market competition and cause resource mismatch.It further weakens the market innovation ability and adversely affects high-quality economic growth [36].
Social inclusive development.The digital economy has an intense color of inclusive benefits, which not only improves the coverage of services and the depth of user use but also reduces related transactions and operating costs.The digital economy directly provides rural residents with financial services such as personal finance, education savings insurance, and express payments.It offers financial support to township enterprises, which is conducive to narrowing the urban-rural development gap.Research demonstrates that, bolstered by advancements in fintech, the digital economy can offer farmers accessible financing avenues via crowdfunding and innovative payment systems.This approach significantly improves the financial and distribution sustainability of agriculture [37].Therefore, in terms of social inclusion, the digital economy has played a positive role in narrowing the urban-rural development gap.However, a heightened level of digitalization may inadvertently facilitate the monopolization of information resources by a few dominant enterprises.This trend is detrimental to the unfettered circulation and efficient distribution of market resources, potentially leading to a decline in overall factor productivity [38].Some scholars have found that the digital divide brought by the development of the digital economy will also lead to the urban-rural development gap, which is not conducive to the inclusive development of society [39].In addition, the development of the internet also provides channels for cybercrimes and illegal digital trade, which may be detrimental to the stability of social order and harm the social welfare of consumers [40].
Low-carbon ecological development.Digital technology is increasingly permeating traditional industries, driving advancements in green technology and fostering sustainable practices.For instance, in the field of agriculture, the dual goals of carbon neutrality and reduction are reshaping rural revitalization.These evolving objectives are aligning with the demands of the modern era, emphasizing the need for sustainable agricultural practices that align with environmental goals.To date, the digital economy has continuously provided technical support for the pilot work of "two-right" mortgages in rural areas [41], creating conditions for large-scale and modernized agricultural production.The integration of digital technology into rural landscapes has notably mitigated the issue of information asymmetry.By harmoniously blending digital innovations with agricultural practices, there's a significant potential to revolutionize agricultural insurance and its financial derivatives.This evolution can broaden the application of agricultural insurance, enhance the green financial framework, and steer the progression towards sustainable, green agricultural practices [42].In terms of industrial development, first, the digital economy can effectively reduce the cost of searching, trading, matching, and copying, thus reducing transaction barriers by alleviating information asymmetry and thereby breaking the market boundary [43].Second, according to demand theory, with the increase in consumer demand for green products, the price mechanism will eventually help promote the change in green production technology innovation and production mode and force innovation subjects to realize demand-oriented green innovation.Third, the digital economy changes people's way of life and raises people's standards in terms of environmental quality, forcing enterprises to make green innovations [44].Therefore, the development of the digital economy can optimize resource allocation by promoting industrial structure upgrading, promoting factor flow, promoting green innovation, and improving energy efficiency, thus promoting regional LCID.However, the expansion of digital technology development may cause the rebound effect of energy demand growth to outweigh the positive impact, leading to more serious environmental pollution [45].When some enterprises use the digital economy to break technical barriers, they will also increase the availability of resources, further exacerbating the loss of resources and further aggravating carbon emissions and environmental pollution.The spread of digital technologies is also likely to stimulate an increase in energy demand, resulting in an energy rebound effect that outweighs its early savings and increases emissions of pollutants and greenhouse gases.Based on the above analysis, we propose a hypothesis:

H1:
The digital economy has an inverted U-shaped impact on LCID

Spatial spillover effect of the digital economy
The development of the digital economy is based on interconnection.Consider that the internet satisfies the "Metcalfe law" of the internet, which shows that the value of a network is equal to the square of the number of nodes in the network.Consequently, the advantages of the internet are poised to grow exponentially in tandem with the rising number of its users.Current research underscores the internet's pronounced externalities and its capacity for generating positive feedback loops.This phenomenon indicates that as internet usage expands, its benefits magnify, not just linearly, but at an accelerating rate, underscoring its far-reaching impact on users and society at large [46,47].First, using the internet platform to communicate is a new way to establish interpersonal relationships and participate in social groups.The advent of this new medium significantly boosts the autonomy, flexibility, and ease of social choices, thereby fostering a comprehensive enhancement in social inclusivity.Furthermore, the evolving functionalities of internet platforms continuously draw in new users, fueling a cycle where the expansion of the network's value generates positive feedback.Large-scale networks leverage their size to perpetually attract fresh users, thereby progressively amplifying the network's spatial influence [48].As an increasing number of users are gathered together, the sense of collective belonging and participation of individuals in the network is also increasing daily, and user stickiness is significantly increased, making the social network more solid [49,50].Third, the digital matching mechanism can give users access to hidden, hard-to-find resources.With the empowerment of digital elements, the openness and inclusiveness of the sharing economy have been significantly improved, and each individual in the network has gained a digital channel to communicate with the surrounding environment.In this way, users can exchange and share idle resources (technology, goods, etc.) quickly and conveniently without being restricted by location and distance, which dramatically reduces transaction costs.Moreover, thanks to the digital security mechanism, users' transactions on the digital platform can cultivate mutual trust [51].Finally, the construction of digital infrastructure can effectively expand the coverage and access depth of the sharing economy.The scale efficiency generated from it is the concentrated embodiment of the externality of the digital economy.Thanks to the empowerment of automation, the quality of digital products will also improve with the expansion of the network so that the evolution of the network can result in positive feedback to the network itself [52].
Therefore, in the process of integrating digital elements with different industries and fields, cross-temporal information dissemination, data creation, and significant sharing reduce transaction costs.The development of the digital economy helps realize the close connectivity between cyberspace and physical space, condenses the spatial and temporal distance through efficient information transmission, and enhances the breadth and depth of interregional economic activities [53][54][55].Therefore, digital development has a significant spatial spillover effect [56,57].Some scholars study China's information infrastructure and find that the economic growth of one region benefits from information exchange and knowledge agglomeration brought by information infrastructure construction in two areas [58].Other studies conclude that internet development has noticeable spatial spillover [55].Because digital economy development promotes economic growth with knowledge accumulation characteristics of R&D personnel flow and capital flow, making a lot of knowledge, technology, and information gathered in the space, the interaction and communication between the main innovation subject can accelerate the diffusion of knowledge and technology, forming a useful complementary knowledge, and helping regional low carbon inclusive growth.In addition to the positive spatial spillover effect, the competition or monopoly effect will also occur.Limited space and market sharing will increase the competitive pressure on enterprises in agglomeration areas.On the one hand, the competition effect will stimulate more "catch-up" innovation vitality.However, some digital enterprises, with their unique advantages in information technology and cost, may form a market monopoly and impact the real economy, while platform enterprises may exercise monopoly market power, which may lead to market non-integration and ultimately may not be conducive to LCID [36].Therefore, we speculate that the digital economy should have two kinds of spatial spillover characteristics to LCID.Based on the above analysis, this paper proposes the following hypotheses.
H2: There are spatial spillover effects of the digital economy on low-carbon inclusive development.

Metrological model
4.1.1.U-shaped econometric model.Initially, drawing from our current research and analysis, we conclude that the digital economy exerts a beneficial influence on sustainable development.However, certain scholarly analyses indicate that the growth of the digital economy might adversely affect the environment.To more holistically assess the environmental implications of the digital economy, we intend to substantiate the theoretical analysis and hypotheses presented in this paper through a nonlinear model.Building on this foundation, we propose to construct the following nonlinear econometric model ( 1) In model (1), LCID represents the low-carbon inclusive development Index of Province I in period T; digi represents the comprehensive digital economy index of province I in period T, and vector X it represents a series of control variables.μ i denotes the fixed effect of the region I that does not change with time, λ t represents the time-fixed effect, and ε it represents the random disturbance term.

Threshold model.
The impact of the digital economy on regional LCID may have a threshold effect.We draw on the study of Hansen [59].To build the following threshold model (2).
Where I (�) represents the function, which is assigned 1 if the conditions in parentheses are true, and 0 otherwise.φ and ϑ are the threshold values to be estimated, while θ and δ are the corresponding estimated coefficients of each variable.The above two models are all set as single threshold models, which can be expanded to multi-threshold scenarios according to steps such as the quantitative test of sample data.
In Formula (3), LCID stands for regional low carbon inclusive growth Index; σ 0 is a constant term; ρ is spatial autoregression coefficient; W is spatial weight matrix, and digi is regional digital economy development water.α1 represents the elastic coefficient of the digital economy's impact on LCID, and β1 represents the coefficient of the digital economy in spatially related regions.X is a series of control variables, α c is the elastic coefficient of the control variables; β c represents the elastic coefficient of influence of spatially correlated regional control variables on regional LCID.ε it represents the random error term.

Spatial weight construction.
Reilly proposed Riley's Law in 1931, which states that the amount of retail trade a city attracts from surrounding towns is proportional to the size of the city's population and inversely proportional to the square of the distance.Later, Walter proposed that inter-regional economic ties depended on regional industrial structure and were affected by the income of other regions, and distance would weaken economic ties [61].Since Hawtrey applied the gravity model to the classical study of international trade, the model has been widely used in many social sciences, such as global economy, economic geography, spatial economy, urban network, etc., and has developed like a fire, and many epoch-making research results have emerged [62].
The purpose of the spatial gravity model is to study the correlation between local and adjacent areas and the determinants of flow levels.Suppose that the geographic space has N spatial units, where Q i , D j , and F (i, j) represent the origin function, objective function, and spatial separation function, respectively.Then the average interaction level between Qi and Dj can be expressed as O(i, j) = C * O(i) * D(j) * F(i, j).N spatial observation units paired with local and neighboring areas can be described as a matrix, as shown in Eq (4): The N*N matrix M represents the pairwise paired Q-D flow.The correlation between local and neighboring places can be divided into local adjacency, neighborhood adjacency, and double adjacency, with different weight Settings for different adjacency cases.
Lesage pointed out that it was wrong to use point estimation to test the spatial spillover effect, and proposed a partial differentiation method to make up for the deficiency of point estimation in measuring the spatial spillover effect [63].SDM is incorporated into the Sieff matrix, and the spatial effect is decomposed into direct effect, indirect effect, and total effect.Convert the general form of the SDM model into: Eq (5) can be transformed into the following matrix equation: That is: . . .
In Formula ( 7), the elements on the diagonal of the matrix reflect the direct effect: direct = @Y i /@X im = H m (W) ii .Elements on the non-diagonal line reflect the spillover effect: The digital economy is one kind of knowledge economy, so the spatial spillover effect of it can be regarded as a kind of knowledge spillover.This paper will construct the R&D personnel spillover weight matrix and R&D capital spillover weight matrix to represent the spatial weight matrix of knowledge spillover.The specific construction method is as follows: In Formula (8), rdl i and rdl j are the total numbers of R&D personnel in the region I and region j respectively.D ij is the distance between region I and region j, which is measured by the spatial distance between cities of provincial capitals.Similarly, by changing the number of R&D personnel in Eq (8) into R&D capital stock, the weight matrix of R&D capital stock can be obtained, as shown in Eq (9).The specific parameters are not described here.

Low-carbon inclusive development (LCID).
Drawing from the current body of literature, this study posits that the transition to a low-carbon economy is steered by a commitment to low-carbon principles, grounded in the pursuit of high-quality economic development.This involves shifting from an extensive, resource-intensive economic model to a more efficient, low-carbon-intensive approach.The goal is to simultaneously advance "carbon reduction, pollution abatement, green growth, and overall economic expansion."Ultimately, the aim is to realize the high-quality development objectives of a low-carbon economy.On the measurement of low-carbon transition development, most scholars measure low-carbon efficiency from the perspective of input-output efficiency, and measure the degree of low-carbon transition [64], while some scholars use low-carbon pilot policies or carbon emission levels to measure low-carbon transition [30,65].According to the research of existing scholars, this paper integrates the concept of inclusiveness into low-carbon development to highlight the connotation of high quality.According to the research of existing scholars, this paper integrates the concept of inclusiveness into low-carbon development to highlight the connotation of high quality [66,67].In the realm of existing literature, approaches like subjective weighting or principal component analysis (PCA) are commonly employed to determine index weights.However, the subjectivity inherent in these methods can significantly diminish their objectivity.Additionally, the interpretational clarity of the comprehensive evaluation function becomes ambiguous when the factor loadings in PCA are negative.The fixed base difference entropy weight method merges the strengths of both the fixed base difference and the entropy weight methods.This technique accounts for time trends, resulting in measurement outcomes that are more objective and reasonable.This paper begins by exploring the fundamental concept of LCID (Low-Carbon Intensity Development) and employs the fixed base difference entropy weight method to devise a comprehensive index system for LCID.We ultimately chose 66 typical indexes, to measure the low carbon inclusive growth of 30 Chinese provinces' composite index (LCID).We will explain the selection of indicators from three aspects: economic growth, social inclusion, and low-carbon development.The comprehensive index system is shown in S1 Table of S1 File.
Economic growth includes three modules: economic growth capacity, economic growth potential, and economic growth quality.Among them, investment, consumption, and export are the "troika" driving GDP growth.Therefore, the share of investment stock, consumption expenditure, and net export are adopted to reflect the economic growth capacity.Besides, the transformation of the economic development pattern, the adjustment of the economic structure, and the release of economic growth potential are inseparable from the basic elements of innovation.Therefore, the indicators of economic growth potential include the stock of human capital, the input, and output of innovation, and the degree of industrial advancement.Since the structure effect and technology spillover effect of FDI can make the industry gradually advance, promote the absorption of foreign advanced technologies, and enhance green innovation ability, the proportion of FDI is included in the system.Social stability is a prerequisite for economic growth.Therefore, the degree of economic fluctuation and consumer price index are further added to reflect the stability of the social environment in the module.To sum up, we use the stock of human capital, the input and output of innovation, the proportion of FDI, the degree of industrial advancement, the degree of economic volatility, and the consumer price index to reflect the potential of economic growth.We have included the per capita GDP, labor productivity, and GDP growth rate in the economic growth framework to reflect the level of economic growth.
Social inclusion mainly represents a kind of social harmony and fairness.Social inclusion includes four modules: fair opportunity, social security, public infrastructure construction, and social inequality.Among them, fair opportunity includes three basic rights: the right to subsistence, employment, and education.Social security covers six indicators: unemployment security, work-related injury security, maternity security, medical security, old-age security, and housing security.Public infrastructure construction includes traditional hardware of hard infrastructure (including transportation line length, fiber optic cable line length, and the number of per capita public toilets) based on education and science and technology research and development and the soft infrastructure is represented by two indexes (including mobile phone and fixed phone users scale, software business income, per capita library ownership).Social inequality covers disparities in sharing the fruits of development between urban and rural areas, between regions, and between rich and poor.
Low-carbon ecological development covers five modules: low-carbon production, low-carbon consumption, ecological livable, ecological endowment, and ecological governance.Among them: low-carbon production includes production consumption and production emissions; Production consumption consists of energy consumption, industrial water consumption, and industrial electricity consumption.Previous studies have shown that the establishment of a resource tax can achieve a win-win situation for the economic and environmental performance of Chinese mining companies.Therefore, manufacturers can reduce carbon intensity while improving total factor productivity, which is conducive to inclusive and low-carbon development [68].Low carbon consumption includes green living measured from three aspects: household water use, harmless domestic waste, municipal sanitation, and green tourism represented by the scale of public transport.Ecologically livable is composed of urban greening and tourism culture.Ecological endowment involves three indexes: coal, water, and forest.Ecological management includes four indicators: soil erosion control, afforestation, geological disaster control, and forest pests and mice.
The steps of the fixed basis entropy weight method for calculating the utilization of the LCID comprehensive index are as follows The first step is to standardize the range of the original data in the t year of China's inclusive green growth index system, to eliminate the inconsistencies in the order of magnitude and dimension of different measurement indicators.
Where i represents province, j represents measure index.x t ij Is a positive indicator, which represents the original index value of inclusive green growth in Chinese provinces in the t year and represents the standardized index value in the T year.max x t ij � � and min x t ij � � represent the minimum and maximum.The second step is to calculate the information entropy of all indicators in the inclusive green growth evaluation system of Chinese provinces.
In Formula (11), when the E t j 2 0; 1 ½ � information entropy is smaller and the dispersion degree is larger, it indicates that the amount of information provided by the index is larger and the weight of the index is larger.Conversely, the weight is smaller.
The third step is to calculate the weight of the inclusive green growth evaluation index of Chinese provinces.
In the fourth step, the initial time of the sample, 2011, was taken as the base year, and the original data were processed by the fixed-base pole-difference method.
Formula (13), X t j represents the dimensionless value of the fixed base error of index J in the t year and x t j is the original value of index J in the t year.x 2011 j;min and x 2011 j;max are the minimum and maximum values of the original data of indicator J in all provinces in the base year respectively.
The fifth step is to calculate the comprehensive index of China's LCID by weighting the index weight.As shown in Eq ( 14)  2022) has a more comprehensive definition of the digital economy, including core production factors such as digital infrastructure, digital industrialization, industrial digitalization, and digital innovation.It becomes evident that as the level of digitalization enhances, the scope and meaning of the digital economy continue to expand, exhibiting a dynamic and evolving trend.Considering the highly pervasive and integrative nature of the digital economy, it is challenging for any single index or dimension to precisely gauge the comprehensive level of the digital economy.Therefore, based on the White Paper of China's Digital Economy Development Report (2020)and referring to the research of existing scholars [20], we compute a comprehensive development index for the digital economy, referred to as 'digi', using the entropy method.This calculation is grounded in the two fundamental aspects of digital industrialization and industrial digitalization.We have constructed four comprehensive index systems to support this: digital infrastructure, digital industrialization, industrial digitalization, and digital innovation, all of which are detailed in S2 (1) Allocation of resources.The development of the digital economy can break down regional barriers and accelerate factor flows, thereby improving resource allocation and promoting LCID.Based on the existing research, we adopt capital utilization efficiency to characterize the efficiency level of resource allocation [69].The capital utilization efficiency is measured as follows: f i indicates the financing cost of industrial enterprises above the provincial scale, and f represents the average financing cost of industrial enterprises above the scale.If misallocation > 0, it means a high resource distortion level.
(2) Profit and loss deviation (Unfairdevelop).The concept of "profit and loss deviation" is focused on the development of resource-based industries, showing the phenomenon that "natural resources are priceless, while resource-based products are cheap".It has produced an imbalance between the ecological environment and economic benefits of "economic benefits are external, ecological damage remains".Based on the existing research, this paper calculates the profit and loss deviation based on the extended Dagum Gini coefficient.The extended Dagum Gini coefficient is the expansion and extension of Dagum based on the traditional Gini coefficient to form a Dagum decomposable Gini coefficient [70], which can deal with the problem of asymmetric heavy-tailed distribution between samples.The basic formula of the Dagum Gini coefficient is shown in (16) and satisfies the formula (17).
The Dagum Gini coefficient can be decomposed into the intra-group Gini coefficient (G jj ) and inter-group Gini coefficient (G jh ).The calculation formulas are ( 18) and ( 19) respectively.
Among them, y ji and y hr represent the profit and loss index of the j region and h region respectively, n represents the total number of provinces investigated n j and n h represents the number of provinces in the j region and h region, k represents the number of divided regions, μ represents the average value of national profit and loss index and Y i represents the average value of profit and loss index in i region.Therefore, this study divides Chinese provinces into 30 groups, discusses the degree of profit and loss deviation between each province and other provinces, and further extends the inter-group Gini coefficient to the formula (20).
4.2.4.Control variable.The control variable will have an impact on the explained variable, which can be intuitively obvious or proved in the literature.Therefore, we refer to the existing research literature and choose from the average economic level, financial level, material basic level of innovation level and the level of opening to the outside world [71][72][73], this paper selects the following control variables: (1) the level of regional innovation (lnrd), measured by the ratio of the number of regional researchers to the total population of each province; (2) the level of economic development (lnpgdp), characterized by the per capita GDP of each province; and (3) the level of financial development (lnfinan), measured by the ratio of the number of deposits and loans to the GDP of each province.(4) material capital level (lnfix), measured by the ratio of infrastructure investment to GDP; (6) urbanization level (lnurban), measured by the number of cities and towns.To improve the comparability between variables, we do logarithmic processing on variables when we return.

Data Sources and descriptive statistics
Data in this paper were collected from the National Bureau of Statistics of China and 30 provincial statistical yearbooks.In addition, part of the energy data comes from the China Energy Statistical Yearbook, China Science and Technology Yearbook, China Labor Statistical Yearbook, (http://www.stats.gov.cn), and China Internet Development status statistical report (https://www.cnnic.net.cn/).Table 1 reports the descriptive statistical results of the variables.As can be seen, the average level of LCID and digital economy in the provinces is low.Besides, regional development indicates the existence of resource misallocation and inequality.

Empirical test
Table 2 shows the empirical results.The column (1) shows that the coefficient of the digital economy is positive but insignificant.The second term is added in columns (2) to (4).The results show that the digital economy has a significant inverted U-shaped impact on low-carbon inclusive development.This observation marks a departure from existing research, which predominantly suggests that the digital economy enhances energy efficiency and innovation.These improvements are typically associated with reducing carbon emissions and fostering sustainable development [4,22].However, this study posits that the aforementioned promotional effect might not follow a linear trajectory.Additionally, previous research tends to overlook the resource distortion effect caused by the digital economy, neglecting to consider both the threshold and spatial effects [74].Distinct from prior literature, this paper primarily explores the impact of the digital economy on low-carbon inclusive development through the lenses of resource misallocation and carbon emission inequality.Consequently, this different analytical perspective leads to divergent conclusions [75].The estimation results from columns (2) to (4) show a threshold for the development of the digital economy.Within the point, the digital economy can promote LCID, while beyond the point, it may have a restraining effect.The economic interpretation of this finding is that for each standard deviation increase in the development level of the digital economy, the level of low-carbon inclusiveness experiences a rise of 2.773%.This signifies a clear positive impact of the digital economy, resonating with assertions made in existing literature [23].Unlike in the past, when the development of the digital economy exceeds a certain extreme point, it has a restraining effect on the level of lowcarbon and inclusive development [21].In this case, the economic meaning shows that for every increase in standard deviation in the development of the digital economy, the level of low-carbon inclusive development decreases by 2.05%.Through statistical analysis, it is found that 92% of the observed areas in China fall into the inverted U-shaped left.However, about 8% of the observations fall on the right side of the inverted U shape.This indicates that in regions where the digital economy is highly developed, potential issues of digital monopolies could emerge.Such monopolies disrupt market competition and obstruct effective resource allocation, adversely affecting LCID.Despite this, the broader influence of the digital economy is significantly positive towards low-carbon and inclusive development.Consequently, policy recommendations should, on one hand, robustly advocate for the growth of the digital economy.On the other hand, they should also intensify the regulation of the digital sector to prevent the emergence of large-scale digital monopolies and harmful competitive practices, which can lead to resource mismatches and environmental inequality.
According to the estimated results of control variables, the level of innovation and economic development is positive but insignificant.The positive and significant correlation between financial development and urbanization levels aligns with practical observations.From a financial development standpoint, a higher level of financial development facilitates the easing of corporate financing constraints.This enables businesses to access more capital, expand production scale, boost employment, and enhance worker welfare.It also supports technological innovation in enterprises and aids in pollution control, particularly in high-polluting industries.As urbanization progresses, public demand for better environmental quality rises.Consequently, some high-energy-consuming industries within cities are relocated to outer areas.The suppression of LCID by the level of material base might be linked to China's tendencies towards over-investment and an extensive production model.

Endogenous test.
(1) Instrument variable method.Drawing lessons from the practice of existing scholars [71], a historical digital circuit was used as an instrumental variable for instrumental variable regression.The results derived from the two-stage least squares method is presented in Table 3.The rationale behind our choice of instrument variable is as follows: we selected the digital circuit infrastructure of each province from the year 1998.This historical variable does not directly influence the current state of low-carbon inclusive development, thereby satisfying the exogeneity criteria.Furthermore, as a form of digital infrastructure in the past, the digital circuit significantly influenced the evolution of today's digital economy.Hence, it is intrinsically linked to the digital economy, fulfilling the requisites for an instrument variable.The instrument variable for this study is formulated by integrating the time variable with the historical instrument variable.The estimated outcomes are detailed in Table 3. Columns ( 1) and ( 2) show that there is a significant correlation between explanatory variables and instrumental variables, and the F value of the first stage is 109.69 and 164 respectively greater than 10, which means that the correlation requirement is satisfied and The there is no problem of weak tool variables.Column (3) shows the results of the second stage estimation.The results show that there is still an inverted U-shaped relationship between the digital economy and LCID after addressing the endogenous problem.Hypothesis H1 is verified.Due to space limitations, the following control variable estimation results are omitted from the table."Control" was used to characterize all control variables.
(2) GMM estimation method.As the estimation method leads to endogenous problems, we use the GMM method for regression, and the results are shown in column (4).The results show that the digital economy has a significant inverted U-shaped impact on low-carbon inclusive development.It shows that there is a "double-edged sword" effect in the digital economy, so the conclusion of this paper is not seriously disturbed by endogenesis.
(3) Change the estimation method.The sample selected in this paper is the panel data of 30 provinces in China, of which data from Taiwan, Hong Kong, Macao, and Tibet are not available and are excluded.Secondly, due to the official launch of the digital financial development index in 2011, the sample time of this paper began in 2011.These may lead to sample selection interception deviation, this paper uses xttobit regression.The estimated results are shown in column (5).The results show that the digital economy has an inverted Ushaped effect on low-carbon development, and the estimated results are robust.

Other robustness tests.
(1) Change measure and data smoothing.The deviation may occur in the process of index measurement, resulting in inaccurate estimation results.Therefore, we replaced the regional low carbon Inclusive Development index measurement method.The estimates are not subject to serious measurement errors.Therefore, we use principal component analysis to reestimate the explained variables, and the regression results are shown in Table 4.The results of column (1) show that the impact of the digital economy on low-carbon inclusive development is still inverted U-shaped.
(2) Smooth treatment.There may be omissions and statistical errors in the process of data statistics, which will lead to unstable estimation.We use truncated software for outlier handling.The estimated results are shown in column (2) of Table 4, which shows that the basic conclusions remain robust.Therefore, it shows that there is no serious outlier interference in the conclusion of this paper.(3) Omitted variable.Due to the possible omission of variations leading to endogenous issues, we added control variables primary education, and information.The education level is expressed by the ratio of undergraduate students in each area to the total population of each province at the end of the year, and the information index is represented by the total number of post and telecommunications services divided by the total population.Column (3) of Table 4 shows that the impact of information resources and education level on low-carbon inclusive development is not significant, and the impact of the digital economy on low-carbon inclusive development is still significant, indicating that the conclusion is robust.

Threshold test of the digital economy.
To further explore the threshold value.We use the threshold model (2) to test.First of all, the impact of the digital economy on LCID may show different characteristics with the level of the digital economy and inclusive growth.Table 5 reports the self-sampling test, threshold estimates, and confidence intervals of threshold models with the digital economy as threshold variables.It can be found that when taking the digital economy as the threshold variable, F statistics are significant in the single threshold model at the statistical level of 10%.The threshold value is 0.2403.Based on the consideration of robustness, we retest the digital economy by principal component analysis, and the threshold test is shown in Table 5.The conclusion shows that there is a single threshold effect in the digital economy.To show the threshold effect intuitively, we verify that there is a single threshold effect in the digital economy through the LR graphic display, as shown in Fig 1 The panel threshold regression outcomes for the digital economy threshold test are detailed in Table 6.Using the digital economy as the threshold variable, the estimated effects are showcased in column (1) of Table 6.This analysis highlights the threshold adjustment role played by the development of the digital economy on LCID.Specifically, when the digital economy is at a lower stage of development, it exerts a positive influence on LCID.With the continuous improvement of the digital economy index, the digital economy plays a significant role in promoting LCID.However, when the threshold value was 0.2377, the promoting effect would be reduced.For robustness, we use principal component analysis to measure the digital economy, as shown in Table 5.It still shows that the development of the digital economy exists within a double threshold value.The double threshold values are 0.1987 and 0.2132.It shows that the result of the digital economy double threshold estimation is robust.The estimation results are shown in Table 6 column (2).7 presents the sampling outcomes with LCID as a threshold variable.The analysis reveals that when LCID serves as the threshold variable, the F-statistics are significant in the double threshold model, yet they are not significant in the triple threshold model.The identified double threshold values stand at 0.3351 and 0.2329.For a more intuitive understanding, we have illustrated the threshold effect in LCID through a graph, depicted in Fig 2 of S1 File.This visualization clearly demonstrates the presence of a double threshold effect in LCID.The literature on threshold effects analysis in low-carbon transition development is scarce, which marks one of the distinctions of this study from previous research [6].This scarcity benefits a more comprehensive analysis of the environmental effects of the digital economy.We posit that there should also be a threshold in low-carbon development.Initially, when the level of low-carbon development is low, the growth of the digital economy might accelerate total energy consumption, which is detrimental to low-carbon development.However, once a certain level is surpassed and the overall environmental focus shifts towards prioritizing low-carbon development, the digital economy then increasingly aims to refine the extensive economic model, thereby facilitating low-carbon development.
The estimated results using LCID as a threshold variable are shown in column (3) of Table 6.It shows that when the level of LCID is low, the digital economy is not conducive to promoting regional LCID.However, with the improvement of the level of regional development, people have higher and higher requirements for environmental quality and social equity.Meanwhile, the positive effects brought by digital technology gradually exceed the adverse impact.It shows that after exceeding a certain threshold, with the deepening of LCID, the promoting effect of the digital economy on LCID is also gradually enhanced.Based on robustness considerations, we measured the LCID index using principal component analysis, as shown in Table 5.The results of threshold values are shown in Table 7.It shows that after exceeding a certain threshold, with the deepening of the degree of LCID, the promoting impact of the digital economy on LCID is gradually enhanced.It shows that the conclusion of the double threshold is still robust.

Threshold is time-invariant.
To verify that the threshold value is not affected by time, we conducted the quantile regression test.Table 8 reports the results of the quantile regression estimates.Column (1) shows that at the 25% quartile, the digital economy has a significant inverted U-shaped impact on LCID.With the LCID level at 50% and 90%, the digital economy still has an inverted U-shaped impact on LCID.This indicates that before the threshold value, the digital economy has a significant role in promoting LCID.When the threshold is exceeded, the impact of the digital economy on LCID has a dampening effect.It can be seen from the changing trend of the coefficient that within the threshold value, the digital economy has a marginal increasing effect on promoting LCID.It shows that the threshold effect of the digital economy is not seriously affected by time.The threshold test is robust.
To show the quantile regression results visually, we show them by drawing.Fig 2 of S1 File shows the impact of the digital economy on low-carbon inclusive development in different quantiles.It can be seen that there is a positive correlation between the digital economy and low-carbon inclusive development, indicating that the digital economy plays a positive role in promoting low-carbon inclusive development.The square term of the digital economy has a negative correlation with low-carbon inclusive development, indicating that beyond a certain threshold, the digital economy has a certain inhibitory effect on low-carbon inclusive development.It further verifies the inverted U-shaped impact of digital economy on low-carbon inclusive development in the benchmark conclusion.
5.3.4.Regional heterogeneity test.We are based on the new situation of China's economic and social development.China can be divided into four major economic regions: eastern, central, and western.In addition, according to the geographical location of Chinese provinces and cities, the samples are divided into coastal and inland areas.On this basis, regional grouping estimation is carried out.The estimated results are shown in Table 9.The test results for the eastern, central, and western regions are shown in columns (1) to (3).Compared with the western region, digitization has a more significant impact on the eastern and central regions.In addition, we can divide the samples into coastal and inland groups.The  results are shown in columns (4) and columns (5) in Table 9.The results still show that the inverted U-shaped impact of the digital economy on coastal areas is more significant.5.3.5.Heterogeneity test of factor productivity.We believe that regional factor productivity level directly affects resource utilization efficiency, which may affect the carbon emission reduction effect of the digital economy, economic growth effect, and social inclusion effect.Therefore, we test factor productivity in groups, and the estimation results are shown in Table 10.The positive impact of the digital economy on LCID in low-productivity regions is more significant.However, if the development of the digital economy exceeds the threshold, digital technology will increase total energy consumption or lead to a mismatch of capitallabor factors, thus inhibiting LCID.

Mechanism analysis
In addition, the development of the digital economy affects the allocation of resources, which is directly related to the rate of return of regional input, which we call "profit and loss deviation", but the benefits brought by the development of the digital economy are greater than the   losses.To test that "resource allocation" and "profit and loss deviation" play a role in the mechanism.Based on the model (1), we construct the following mechanism models ( 21) and (22).
In model (21) and model (22), Mechanism is the mechanism variable, which represents resource allocation (misallocation) and profit and loss deviation (Unfairdevelop) respectively.The interpretation of other parameters in the model is consistent with that of the model ( 1), and we will not repeat it.We focus on the symbol and significance of the coefficientγ 2 and γ 3 in model ( 21) and the coefficient δ 2 in model (22).

Resource allocation.
According to theoretical analysis, we construct the resource mismatch index as the reverse proxy variable of resource allocation.The verification results of resource allocation as a mechanism variable are shown in columns ( 1) and ( 2) in Table 11.Column (1) reports the regression results of the digital economy to resource allocation.It shows that within the threshold, the digital economy can play a positive role in improving the efficiency of resource allocation.But beyond the threshold, the digital economy can also exacerbate resource misallocation.Column (2) shows that there is a negative correlation between resource mismatch and LCID.It is not statistically significant, but it can be proved that the misallocation of resources is not conducive to low-carbon inclusive development.Therefore, we believe that the resource allocation effect plays a mediating role.
5.4.2.Profit and loss deviation.The connotation of profit and loss deviation shows that with the continuous exploitation of natural resources in resource-based areas, they will not only face the depletion of natural resources and lose the development value of natural resources but also face solving the severe problems left over from exploitation.According to the theory of ecologically unequal exchange, these pollution costs are not calculated in the price of resource-based products, that is, they are exogenous in product prices, resulting in a profit and loss deviation phenomenon of "economic benefits outside and ecological damage included".As a result of inter-regional economic development, the ecological environment is a relatively unfair, uncoordinated state.The development of the digital economy can promote the flow of factors and alleviate the imbalance of regional development, thus alleviating the deviation between profit and loss.This paper tests the mechanism according to the profit and loss deviation as a mechanism variable.The estimated results of column (4) in Table 11 show that there is a negative correlation between profit and loss deviation and LCID.Column (3) in Table 11 demonstrates that the digital economy has a significant U-shaped impact on the profit and loss deviation, indicating that within the threshold, the digital economy can alleviate the deviation of regional profit and loss and improve the level of LCID.However, exceeding the threshold may inhibit LCID by exacerbating the degree of loss and profit deviation.

Spatial correlation
According to theoretical analysis, the digital economy helps to promote the flow of information and factor resources between regions and increase spatial relevance.This means that spatial spillover may exist.We think that the factor resources it brings are a kind of knowledge factor resource flow.In this paper, R&D personnel and R&D capital flow are used to represent knowledge elements.First of all, by constructing the spatial weight matrix of R&D personnel spillover and R&D capital spillover, the Moran index of the digital economy and LCID (Moran's I) is calculated.The results are shown in Table 12.
In addition, through the LM test, it is found that the P values of spatial autoregression and spatial lag test are both less than 0.001, indicating that the spatial model should be used instead of using OLS estimation.

Spatial empirical analysis
6.2.1.Weight matrix of basic R&D personnel.Through the F test and Hausmann test, this paper finally chooses the spatial fixed-effect model for estimation.The specific estimates are shown in Table 13.Table 14 reports the estimation results of the spatial autoregressive certain spatial correlation.In addition, the coefficient of digi is significantly positive, while digi2 is significantly negative.This indicates that the influence of the digital economy on lowcarbon industrial development (LCID) exhibits non-linear spatial characteristics under the spillover effect of researchers.This impact is shaped not only by local R&D talent but also by the knowledge spillover effects arising from the mobility of R&D personnel.Since R&D personnel possess specialized knowledge, their impact on the development of the digital economy is considerable.However, the low mobility of these professionals limits the extent of knowledge-based spatial spillover, rendering this effect relatively subtle in practice.

Based on the weight matrix of R&D capital.
According to most estimates in Table 14, shows that under the effect of scientific research capital spillover effect, the development of the digital economy has a spatial spillover effect, and according to the square term of the digital economy, the development of the digital economy has an inverted U-shaped spillover effect.The spatial spillover effect of the digital economy may be mainly due to the flow of scientific research capital.Under the estimation of the spatial Durbin model, the spatial effect is not statistically significant, yet a nonlinear trend is still discernible.To ascertain the precise influence of this spatial effect, we proceed to conduct a spatial decomposition analysis in the subsequent section of the article.The foregoing suggests that the impact of the digital economy on low-carbon transformation and development might exhibit spatial effects, necessitating further empirical testing for confirmation.

Test of fitting effect of spatial model.
To further evaluate and compare the fitting efficacies of three spatial econometric models, this study conducts Ward and LR tests, the results of which are detailed in Table 15.In the spatial weight matrix of R&D personnel and R & D capital, the spatial fixed effect, time fixed effect, and Spatio-temporal double solid effect all pass the 1% significance test, rejecting the original hypothesis, indicating that the spatial Doberman model (SDM) can not be transformed into SAR model and SEM model.Then compare the adjusted decision coefficient R2 of the spatial Durbin model (SDM) (Tables 13 and  14).We find that the estimation effect of the spatial Durbin model is relatively optimal under the spatial fixed effect.Therefore, we finally choose to use the spatial Durbin individual fixed effect model as the analysis basis of the spatial benchmark regression results.
6.2.4.Spatial effect decomposition.According to the partial differential method put forward by Lesage et al. [63], the influence effect of the digital economy on LCID is decomposed into direct effect, indirect effect, and total effect.The specific estimation results are shown in Table 16.Column (3) presents the estimated outcomes for the total effect within the overflow weight matrix linked to R&D personnel.This illustrates that, influenced by the spatial spillover of R&D personnel, the digital economy's overall impact exhibits an inverted U-shaped  4) to (6) in Table 16 display the estimation findings under the spatial weight matrix associated with R&D capital spillover.During the initial development phase, the digital economy plays a pivotal role in enhancing LCID and exerts a positive influence on LCID within neighboring regions.However, once the value surpasses the critical point, the digital economy begins to exert a limiting effect on LCID, simultaneously manifesting a negative spatial spillover impact on the surrounding areas.The possible reason is when the threshold is exceeded, it may have a "Hongxi effect" on the R&D capital in the surrounding area, leading to a relative decrease in the R&D capital in the surrounding area.As the digital economy in a given region reaches a certain level of development and its digital infrastructure becomes relatively robust, it tends to attract capital from neighboring areas.This influx can result in a capital deficit in these surrounding regions, adversely affecting their capacity for low-carbon development.

Spatial robustness test
The aforementioned analysis stems from the outcomes of the knowledge factor flow weight matrix.The flow of R&D factors can be attributed to variables like geographical location and economic development level, among others.Presently, there are various weight matrices used to measure spatial distance and economic factors, such as adjacency space weight, distance space weight, and economic distance space weight.The first two are categorized as static spatial weights, while the latter is considered dynamic spatial weights.Adjacency spatial weight relies on the proximity of spatial units to ascertain spatial relevance.However, this approach may not align with the actualities in economic research, as it overlooks other influential factors.With the deepening of research, Tobler believes that everything is associated with surrounding things, and the degree of association depends on the distance of spatial units [76].The commonly used weight matrix of spatial distance is shown in Formula (23).
d is the Euclidean distance of two space units.Considering the heterogeneity of connectivity intensity and influence degree of different regions, adjacency weight, and distance weight consider the spatial relationship of economic activities from geographical proximity factors.Subsequently, many scholars are required to construct the spatial weight matrix from the perspective of economic activities.Some scholars constructed the weight of economic distance with the gravity model, whose basic assumption is that the spatial correlation between two regions is equal.Therefore, the weight of the nested economic distance constructed is shown in Eq (24).
S ij is the distance space weight, Euclidean distance from region i to region j, and represents the per capita GDP of region i in year t.The per capita index is selected to eliminate the influence brought by size.To sum up, we adopt distance spatial weight, economic spatial weight, and economic distance nested spatial weight respectively to analyze the spatial interaction among provinces.The estimated results shown in Table 17 indicate the conclusion that the inverted U-shaped influence of the digital economy has a spatial spillover effect and is still robust under different weight matrices.

Conclusions and discussion
The conclusions are as follows: (1) Our findings indicate an inverted U-shaped correlation between the digital economy and LCID.Notably, the digital economy influences LCID predominantly through two key channels: the optimization of resource allocation and the deviations in profit and loss.As previous studies, we affirm that the development of the digital economy still has a significant positive effect on low-carbon inclusive development [22,77].The conclusions of this paper significantly diverge from previous studies.It examines both the beneficial and detrimental impacts of the digital economy on carbon emissions, offering crucial recommendations for tackling carbon emissions.Technology acts as a double-edged sword; only through judicious application can its positive contributions be maximized.(2) The heterogeneity analysis shows that the digital economy has a more significant impact on LCID in eastern China and regions with lower factor productivity.However, the existing research literature has not found that the environmental effects of digital economy development in areas with low labor productivity are more positive, which enriches the existing research conclusions [78].(3) The analysis of the spatial spillover effect shows that the development of the digital economy has a spatial spillover effect.While prior research has explored the spatial effects of household carbon emissions, this study sets itself apart by delving into the unequal spatial effects of carbon emissions.It highlights how areas with higher emissions impact the emission levels in adjacent regions, consequently imposing increased environmental stress on these neighboring areas.Thus, it underscores the necessity for more refined policies that equitably balance the interests between areas of high emissions and their surrounding regions.This finding offers substantial reference value for the development of policies aimed at ensuring equity in carbon emission rights.Previous studies have also found that the digital economy has positive spatial environment spillover effects [33], but this paper also pays attention to the negative spatial environmental spillover effects of the digital economy, which provides new insights for guiding the development of the digital economy.(4) Through the conclusion of this paper, we explain the applicability of this conclusion: on the one hand, China is a developing country, and our development model is similar to that of most emerging countries, and the development model is extensive to conservation-oriented.Therefore, it can provide experience for other developing countries in the development experience of low-carbon transformation.On the other hand, China is a big digital economy, which can provide technology spillover for countries with extensive development models in using digital technology to reduce carbon emissions, and promote regional sustainable development.For example, due to the spatial spillover digital economy, the promotion of regional digital technology development is conducive to regional low-carbon coordinated development.

Policy implications
1. the government should vigorously develop the digital economy.On the one hand, all regional governments should make great efforts to build digital infrastructure to lay the foundation for the application and development of digital technology.Secondly, the government has issued opinions and policies to encourage the digital transformation of enterprises to promote the digital transformation of enterprises, especially for industries with high energy consumption and high pollution.Finally, strengthen the education and training of digital technology to provide digital talents for the development of the digital economy.
2. strengthen the supervision of the development of the digital economy.Digital technology is a double-edged sword, with equal emphasis on guidance and supervision.Regional governments should issue rules and regulations for the development of the digital economy to provide legal protection for guiding the healthy development of the digital economy.Establish a market supervision committee for the development of the digital economy to crack down on illegal market practices such as malicious competition and price monopoly, and provide new momentum for low-carbon and inclusive development.
3. promote the coordinated development of regional low carbon.The difference in regional resource endowment leads to the inequality of environmental effects brought by the digital economy.The negative externalities of the space environment in industrially developed areas should be actively dealt with, therefore, it is necessary to strengthen inter-regional cooperation in environmental governance.
There are still shortcomings in this paper: For example, according to the existing research, the development of a digital economy may be mainly restricted by the level of technological innovation, so innovation may be an important threshold for the development of the digital economy, and it need further analysis.In addition, the sample should be more miro.China has 691 cities.Although the provincial panel data in this paper contains more index information, each city development has its resource endowment characteristics.Future recommendation: First, the environmental effects of the digital economy deserve more extensive discussion.On the one hand, the digital industry chain is a new research direction.For example, how to promote the green and low-carbon development of enterprises in the middle and upper reaches through the digital transformation of the industrial chain.Second, this paper pays attention to the negative effects of the digital economy, so the double-edged sword effect of the digital economy is worthy of in-depth study.For example, whether the digital divide and digital monopoly hurt the environment is worthy of further study.

.2.3. Mechanism variable.
Table of S1 File.Many indicators' data started in 2009, except for the digital financial indicator's statistics started in 2011.More indicators and longer estimated life may be retained, and we use linear interpolation to make up for the missing values of digital financial indicators.The comprehensive index system is shown in S2 Table of S1 File. 4

Table 12 . Moran's I.
, spatial error model, and spatial Durbin model.Three effects of spatial fixation (SF), time fixation (TF), and Spatiotemporal bidirectional fixation (STF) are reported in each estimation model.From the estimated results, it can be seen that under the three spatial econometric models, most of the spatial autoregressive coefficients and spatial error term coefficients pass the significance test of 1%.Hence, the LCID among provinces in China has a model